Nonstationary panel models with latent group structures and cross-section dependence

This paper proposes a novel Lasso-based approach to handle unobserved parameter heterogeneity and cross-section dependence in nonstationary panel models. In particular, a penalized principal component (PPC) method is developed to estimate group-specific long-run relationships and unobserved common factors and jointly to identify the unknown group membership. The PPC estimators are shown to be consistent under weakly dependent innovation processes. But they suffer an asymptotically non-negligible bias from correlations between the nonstationary regressors and unobserved stationary common factors and/or the equation errors. To remedy these shortcomings we provide three bias-correction procedures under which the estimators are re-centered about zero as both dimensions (N and T) of the panel tend to infinity. We establish a mixed normal limit theory for the estimators of the group-specific long-run coefficients, which permits inference using standard test statistics. Simulations suggest good finite sample performance. An empirical application applies the methodology to study international R&D spillovers and the results offer a convincing explanation for the growth convergence puzzle through the heterogeneous impact of R&D spillovers.